Friday, September 25, 2009

Night racing and Olbers's paradox

It would be easy to think that the existence of night is solely a consequence of the rotation of the Earth and its location relative to the Sun. But it is not. It is a consequence of the expansion of the Universe. If the Universe were not expanding then, wherever we looked into space, our line of sight would end at a star. The result would be like looking into a forest of trees. In a universe that didn't expand, the whole sky would resemble the surface of a star; we would be illuminated by perpetual starlight. What saves us from this everlasting light is the expansion of the Universe. It degrades the intensity of the light from distant stars and galaxies, and it leaves the night sky dark. (John Barrow, The Artful Universe, p45.)

As the Sun sets in Singapore, and European visitors fight the disruption to their circadian cycles, the aesthetics of Formula 1 undergoes a phase transition. A silver strip of metal halide light runs between the colonial palm trees, beneath the bejewelled post-modernist towers, underneath the concrete stanchions of the flyovers, alongside the armadillo-contoured concert hall and theatre, and beside the neoclassical and Palladian civic architecture. Specular reflections shimmer from the compound surfaces of the cars; the Ferraris become molten lava, and the McLarens dissolve into liquid metal.

Permitting this extravagant display of light and pattern is the dark night sky, a phenomenon whose very existence requires a cosmological explanation, as recognized by the 19th century German physician and amateur astronomer, Heinrich Olbers. Olbers realised that if our universe were a static universe, infinite in space and time, and homogeneously populated with stars (or galaxies or galaxy clusters etc.), then the sky should be bright throughout the day and night. The fact that the night sky is dark is therefore Olbers's paradox. Modern physics solves Olbers's paradox by virtue of the fact that light travels at a finite speed, and by virtue of the fact the Friedmann-Robertson-Walker models of relativistic cosmology represent our universe to be an expanding universe of finite age.

In a universe of finite age, in which light travels at a finite speed, there will be a finite cosmological horizon around every astronomically observant species; the universe is 14 billion years old, hence the light from stars more than 14 billion lights years away has not had time to reach us. Moreover, in an expanding universe, the expansion red-shifts distant starlight towards energies invisible to the naked eye, and reduces the brightness of the light.

There is a twist, however, for "it seems that the background of the sky is bright, even at night. Of course, it is not as bright as the surface of the Sun, nor does it shine at the same wavelengths. However, according to models of the big bang, the entire universe was so hot around 14 billion years ago that each of its points was a luminous as the surface of the Sun. Each direction leaving from our eye reaches a point of this past Universe. And by the same reasoning as that of Olbers, even in the absence of every star, we should be surrounded by this enormous bright object, the early Universe...We indeed receive this radiation, but it is shifted towards long wavelengths and weakened...Since it is very old, the shift is very strong: redshifted by a factor greater than 1000, it has transformed the light into microwaves. This electromagnetic fossil radiation, a vestige of the primitive epoch, was detected for the first time in 1964. Today it is being exhaustively observed under the name of cosmological background radiation." (Jean-Pierre Luminet, The Wraparound Universe, p159-160).

This weekend then, the Formula 1 cars will race at night through the streets of Singapore, and will do so oblivious to the omnipresent background radiation, and the cosmological expansion which permits this visual and kinetic cornucopia.

5 comments:

I was at the hole of Holcrum Yesterday, lazying about in the sun and thinking about the Saxon chief Wade who was apparently a giant of a man, and with his big hands scooped up a handful of earth and chucked it at his wife Bell - the soil missed its target and landed to form the 800ft high hill of Blakey Topping.

I suppose we are making progress, but something tells me we have a long way to go yet, better answers seem to throw up even better questions?

Uuhmm.. 1 Why should we be able to see the Big Bang? The light that was emitted at the time of the Big Bang travels at the speed of light. The universe expands at some speed lower then the speed of light. Hence, all the light that was emitted during the Big Bang is OUTSIDE of the boundaries of the physical universe. We can not catch up with this. Or am I missing something?

2 Why should the sky be bright at night? This only makes sense when there is an infinite number of stars. And even then only when the average distance between them is 'not too big'. A star that's further away gives us fewer light, so it is quite obvious why the sky is dark. If the stars were closer together, then the sky would be brighter.

1. The Big Bang was not an explosion outwards into a pre-existing void.

2. Yes, the false combination of assumptions includes the assumption of an infinite population of light sources: Olbers realised that if our universe were a static universe, infinite in space and time, and homogeneously populated with stars... On the issue of the density of the light sources, if you imagine concentric shells of light sources around the observer, the surface area of these shells grows with the square of the radius, whilst the intensity of the observed light from each individual source diminishes according to an inverse-square law, so the two effects balance.

Thank you for answering my layman questions. I could ask all day. If the big bang was the start of matter and of spacetime, then where does the light of the big bang travel to? Does it bounce up and down inside the boundaries of the universe so that we can see it? Does it also mean that outside of the universe there is no empty space, but NOTHING? What is the difference between empty space and nothing? I have a problem imagining the whole thing.

Nothing would be the empty set, whilst empty space is a non-empty set which possesses properties such as cardinality, continuity, and dimension.

The universe isn't represented to possess a boundary in general relativistic cosmology (although this is perfectly possible mathematically). According to general relativistic cosmology, space could be finite without a boundary or infinite without a boundary. The light emitted in the early universe simply travels within the universe.